The Cartan distribution on an infinite jet bundle is the tangent distribution spanned by the total derivative vector fields. These vector fields differentiate the independent variables together with all derivative coordinates in a way consistent with prolongation. Their Lie brackets remain in the distribution, so the Cartan distribution is an involutive distribution.
For a system of partial differential equations, the Cartan distribution restricts to its infinite prolongation. Its integral manifolds are the prolonged graphs of solutions. A diffiety consists of such an infinite-dimensional equation manifold together with this distribution.
